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Abstract
This paper aims to investigate the effect of a non-uniform internal volumetric energy generation on the conjugate MHD natural convection in a square cavity filled by an electrically conducting fluid. The uniform magnetic field is applied horizontally; the two horizontal and vertical left walls are thermally insulated, whereas the right vertical wall is kept at constant cold temperature. The governing conservation equations are solved numerically using an in house program based on the finite-volume method and the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The effects of internal Rayleigh, Hartmann and Prandtl numbers, thermal conductivity ratio, inclination angle of the cavity, and the thickness of heat source partition are discussed. The obtained results show that regardless of Kr, α and Δ, an almost pure conduction state is observed for low RaI without MHD and for high RaI with MHD at high magnetic field intensity.
| Nomenclature | ||
| B0 | = | magnetic field (T) |
| e | = | wall thickness, (m) |
| g | = | gravitational acceleration (m/s2) |
| H | = | cavity height, (m) |
| Ha | = | Hartmann number |
| k | = | thermal conductivity (W/m·K) |
| Kr | = | thermal conductivity ratio |
| L | = | cavity length, (m) |
| p | = | pressure (Pa) |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| q0″ | = | heat generation (W /m3) |
| Qmax | = | maximum volumetric energy generation |
| Parameter | ||
| Qt | = | total energy generation parameter |
| RaI | = | internal Rayleigh number |
| T | = | temperature (K) |
| u | = | velocity in x direction (m/s) |
| U | = | dimensionless velocity in X direction |
| v | = | velocity in y direction (m/s) |
| V | = | dimensionless velocity in Y direction |
| x, y | = | Cartesian coordinate (m) |
| X, Y | = | dimensionless Cartesian coordinate |
| Greek symbols | ||
| α | = | thermal diffusivity (m2/s) |
| α | = | inclination of cavity |
| β | = | thermal expansion coefficient (1/K) |
| μ | = | dynamic viscosity (kg/m.s) |
| υ | = | kinematic viscosity (m2/s) |
| σ | = | electrical conductivity (1/Ω.m) |
| θ | = | dimensionless temperature |
| ρ | = | density (kg/m3) |
| Δ | = | dimensionless wall thickness |
| Subscripts | ||
| c | = | cold |
| f | = | fluid |
| s | = | solid |
Disclosure statement
No potential conflict of interest was reported by the authors.